Fourier Analysis of Stationary Time Series in Function Space

• Activity Number: 143
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Shahin Tavakoli*+ and Victor Panaretos
• Companies: EPFL and EPFL
• Keywords: cumulants ; discrete Fourier transform ; functional data analysis ; functional time series ; mixing ; spectral density operator

Abstract

The problem of drawing statistical inferences on the second-order structure of weakly dependent functional time series is considered. Much of the research in functional time series has focused on inference for stationary time series that are linear. We consider the problem of inferring the complete second-order structure of stationary functional time series without any structural modeling assumptions. Our approach is to formulate a frequency domain framework for weakly dependent functional data, employing suitable generalizations of finite-dimensional notions. We introduce the basic ingredients of such a framework, propose estimators, and study their asymptotics under functional cumulant-type mixing conditions. We give examples of functional processes satisfying our mixing conditions, and study the effect of observing the functions on finite grids.